A biased coin was tossed 350 times and the number of tails observed was 178. Calculate the relative frequency of getting heads.
So here we have an experiment where we’re tossing a coin. We’re told that the coin is biased. That means that the outcomes of heads and tails are not equally likely. For example, it could be weighted so that it lands on heads more frequently than tails. We’re asked to calculate the relative frequency of getting heads. This is often referred to as finding the experimental probability of getting heads. Let’s see if we can make sense now of the information that we’re given.
We’re told that the coin was tossed 350 times. We’re also told that the number of tails that were thrown was 178. We can assume that even though we’re told that the coin is biased, that it still has two possibilities, heads on one side and tails on the other side. So we need to work out how many times did heads appear during this experiment. Since we know that our coin must either show heads or tails, then we could say that 178 plus the number of heads would equal 350. So to find the missing number of heads, we could calculate 350 take away 178, giving us 172. So the number of heads that were thrown must be 172.
To find the relative frequency of getting heads, we use the formula: the relative frequency of an event is the frequency of event divided by the total frequency. And since the word frequency refers to the number of times something happened. We can also write this formula as: the relative frequency equals the number of times the event occurred over the total number of trials.
So in our experiment, to find the relative frequency of getting heads when we toss the coin, we calculate the number of heads divided by the total coin tosses. Which would give us the fraction of 172 over 350. And now, we see if we can simplify this fraction. We notice that they’re both even members. So we can divide 172 and 350 by two, which gives us 86 over 175. Since this fraction cannot be simplified any further, then the final answer for the relative frequency of getting heads is 86 over 175.